Calculate the quotient below and give your answer in scientific notation. ${\dfrac{1.88\times 10^{6}}{2000}} =\ ?$
Solution: First, let's change the number in the denominator into scientific notation. ${\dfrac{1.88\times 10^{6}}{2000}} = {\dfrac{1.88\times 10^{6}}{2.0\times 10^{3}}} $ Start by collecting the significands and exponents. $ {\dfrac {{1.88} \times {10^{6}}} {{2.0} \times {10^{3}}} = {\dfrac{1.88}{2.0}} \times {\dfrac{10^{6}}{10^{3}}}} $ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= {0.94} \times {10^{6 \,-\, 3}}$ $= {0.94} \times {10^{3}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the right without changing the value of our answer. We can use the fact that ${0.94}$ is the same as ${9.4 \div 10}$, or ${9.4 \times 10^{-1}}$. $ = {9.4 \times 10^{-1}} \times {10^{3}} $ $ = 9.4 \times 10^{{-1} + {3}} $ $= 9.4\times 10^{2}$